Boundary conditions for the infinite square well: These slides make the case for the boundary...

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Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit of large well depths for the finite square well. The finite square well wavefunctions were computed using an application found at http://webphysics.davidson.edu/faculty/dm b/SingleWells/Well2.html

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Transcript of Boundary conditions for the infinite square well: These slides make the case for the boundary...

Page 1: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Boundary conditions for the infinite square well:

These slides make the case for the boundary conditions for the infinite square well by taking the limit of large well depths for the finite square well.

The finite square well wavefunctions were computed using an application found at

http://webphysics.davidson.edu/faculty/dmb/SingleWells/Well2.html

http://webphysics.davidson.edu/faculty/dmb/SingleWells/Well2.html
http://webphysics.davidson.edu/faculty/dmb/SingleWells/Well2.html
Page 2: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Boundary conditions for infinite barrier:

continuous

can be discontinuous at the barrier edge

under the barrier

x

0

Page 3: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Note that the y axis only shows units of energy. No units are show for the wavefunction, which is ok since all that matters is that the probability is normalized to unity.

Page 4: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 5: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 6: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 7: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 8: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 9: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 10: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 11: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Boundary conditions for infinite barrier:

continuous

can be discontinuous at the barrier edge

under the barrier

x

0

Page 12: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Intuition about the central barrier

Page 13: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 14: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 15: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 16: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 17: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 18: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 19: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 20: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 21: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 22: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.
Page 23: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Boundary conditions for infinite barrier:

continuous

can be discontinuous at the barrier edge

under the barrier

x

0

Page 24: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Additional discussion about normalizability

Key point: There exist “energy eigenstates” for the finite square well with continuous values of the eigenvalue E. These states are only excluded by the requirement that the wavefunction be normalizable.

Page 25: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09

Page 26: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0901

Page 27: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0902

Page 28: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09021

Page 29: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09022

Page 30: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09023

Page 31: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.090234

Page 32: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.090235

Page 33: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.090237

Page 34: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09023772

Page 35: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.090237735

Page 36: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0902377385

Page 37: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0902377388

Page 38: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0902377395

Page 39: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0902377399

Page 40: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09023774

Page 41: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09023775

Page 42: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09023776

Page 43: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09023778

Page 44: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0902378

Page 45: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0902379

Page 46: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.090238

Page 47: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.090239

Page 48: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09024

Page 49: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09025

Page 50: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09026

Page 51: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09029

Page 52: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0904

Page 53: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.0907

Page 54: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.092

Page 55: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.094

Page 56: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.097

Page 57: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +36.09

Page 58: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +48

Page 59: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +55

Page 60: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +60

Page 61: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +65

Page 62: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +70

Page 63: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +75

Page 64: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +80

Page 65: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Energy = +81.176

Page 66: Boundary conditions for the infinite square well: These slides make the case for the boundary conditions for the infinite square well by taking the limit.

Acoustic performance of industrial mufflers with CAE ... · PDF fileSYSNOISE for analysis. ... acoustically infinite impedance. To give the infinite impedance boundary condition to

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